Relating lines to planes
Lesson 6.1
Plane
Two dimensions (length and width)
No thickness
Does not end or have edges
Labeled with lower case letter in one corner
m
Coplanar
Points, lines or segments that lie on a plane
B
A
m
C
Non-Coplanar
Points, lines or segments that
do not lie in the same plane
A
B
m
C
Definition:
Point of intersection of a line and a plane is called
the foot of the line.
B is the foot of AC in the plane m.
A
B
m
C
4 ways to determine a plane
1. Three non-collinear points determine
a plane.
n
One point - many planes
Two points - one line or many planes
Three linear points - many planes
2.
Theorem 45: A line and a point not
on the line determine a plane.
3. Theorem 46: Two intersecting lines
determine a plane.
4. Theorem 47: Two parallel lines
determine a plane.
Two postulates concerning lines and planes
P1: If a line intersects a plane not
containing it, then the intersection is
exactly one point.
X
C
m
Y
P2: If two planes intersect, their
intersection is exactly one line.
n
m
1. m Ո n = AB
___
2.
3.
4.
5.
6.
7.
8.
9.
m
A, B, and V determine plane ___
Name the foot of RS in m. P
n
AB and RS determine plane ____.
R or S determine plane n.
AB and point ______
Does W line in plane n? No
Line AB and line ____
VW determine plane m.
or P are coplanar points.
A, B, V, and W
_______
A, B, V, and R______
or S are noncoplanar points.
Given: ABC lie in plane m
P
PB  AB
PB  BC
A
B
C
m
1.
2.
3.
4.
5.
6.
7.
PB  AB, PB  BC
PBA & PBC are rt s
PBA  PBC
AB  BC
PB  PB
ΔPBA  ΔPBC
APB  CPB
AB  BC
Prove: <APB  <CPB
1.
2.
3.
4.
5.
6.
7.
Given
 lines form rt s
Rt s are 
Given
Reflexive Property
SAS (4, 3, 5)
CPCTC